Superconductor compositions operable at high temperatures

ABSTRACT

The composition of compounds containing a multiplicity of different elements are optimized in general by full or partial substitutions of one or more of the atoms in such compounds so as to effect an Ne/χ value which represents a peak or near peak value in λ (the electron-phonon coupling constant) so as to maximize T c  for such compositions of matter.

FIELD OF THE INVENTION

This invention relates to superconductor materials and in particular to compositions that result in superconductive characteristics at relatively high temperatures.

DESCRIPTION OF THE PRIOR ART

The Phenomenon of superconductivity occurs with certain metals and alloys when cooled to a very low characteristic transition temperature, superconductive elements, alloys or compounds will conduct electricity without resistance below a critical temperature T_(c). Resistance is undesirable because it causes loss in energy flow through the material. Superconductivity, which was first discovered by Onnes in 1911, is characterized by the disappearance of all electrical resistance in a material below the transition temperature.

Superconductor materials have been found to be useful for various applications, such as superconducting magnets, magnetic resonance imaging, high sensitivity bolometer, and magnetoencephalography, among others. However, a major problem is the necessity to operate the superconductor material at a very low temperature, such as 4.2° K, which would require the use of liquid helium for example. Large and costly equipment is required and maintenance and repair are major problems.

In the article “Theory of Superconductivity” published in Physical Review, Dec. 1, 1957, page 1175, Bardeen, Cooper and Schrieffer proposed a theory of superconductivity (known as the BCS Theory) that delineates the properties of superconductors. The theory postulates that the interaction between electrons resulting from a virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy. The BCS theory, for which they were presented with a Nobel Prize in Physics, expresses the relation between T_(c), a typical phonon energy (ω), and the interaction strength N(O)V as

T _(c)=1.14(ω)exp[−1N[O]V]

This BCS equation for T_(c) has been modified to include μ*, the coulomb pseudopotential. The modified equation

T _(c)=1.14(ω)exp[−1/N[O]−μ*].

It should be noted that in the framework of the BCS theory, there is a formula for estimating the T_(c). However, it is a general formula which does not take into account any specific feature of the superconducting materials.

In the 1975 publication by Allen-Dynes, Physical Review B, Vol. 18, #3, page 913, the value of μ* is treated as a constant of 0.10, which value will be used in the explanation of the present invention.

In pages 75-77 of the text of Volume 21 of Physical Chemistry, published by Academic Press, R. T. Sanderson sets forth a principle of electronegativity equalization. The principle is that “When two or more atoms are initially different in electronegativity combine chemically, they become adjusted to the same intermediate electronegativity within the compound”. The intermediate electronegativity may be defined as the geometric mean of the individual electronegativities of all of component atoms that make the compound formula. For example, if the A₂B₃ represents a compound of two atoms of A and three atoms of B, the electronegativity may be expressed as

χ_((A2B3))=(χ² _(a)χ³ _(b))^(1/5)

Andre Mourachkine points out in the text “Room-Temperature Superconducitivity”, published in 2004 by International Science Publishing, at pages 21-22, that there is no theoretical formula for predicting the value of critical temperature in a given compound and that there is no rule for predicting whether a certain substance will undergo a superconducting transition at a particular temperature. The publication points out that a major problem in the field of superconductivity is how to calculate the critical temperature T_(c) value in different materials by taking into account the specific features of a material.

In an article “Transition Temperatures of Strong Coupled Superconductors” by W. L. McMillan, Physical Review, Vol. 167, pg 334-367 (1968), McMillan provides a set of equations that allows for the calculation of λ values from experimental values of θ_(D) and T_(c) for a wide variety of superconductors. The McMillan article is incorporated herein by reference.

McMillan provides two principle equations:

T _(c)=θ_(D)/1.45exp[1.04(1+λ)/λ−Ξ*(1−0.62λ)]

and λ=1.04 μ*ln(θ/1.45T _(c))/(1−0.62 μ*)ln(θ/1.45T _(c))−1.04

The above equations are solved for a variety of superconductors (elements and compounds) using a constant μ*=0.10. McMillan's equations are valid only for λ values between 0.33 and 0.90. Beyond those limits, error greater than 10% occurs for the calculated λ values.

SUMMARY OF THE INVENTION

An object of this invention is to provide selected superconductor compositions that exhibit superconductivity at relatively high temperatures.

According to this invention novel superconductor compositions are established by taking into account the value of Ne/χ of any arbitrary composition where Ne is the average number of valance electrons in the composition of matter in question and χ is the absolute value of the electronegativity of such a composition. By utilizing prior experimental work by McMillan and Allen-Dynes we establish a new universal relationship which allows for the calculation of λ (electron phonon coupling constant) and, from a universal equation developed from the McMillan and Allen-Dynes publication which is λ=[(ln θ_(D)/2T_(c))/2]⁻¹. From these parameters we can construct the response of λ (electron-phonon coupling constant) to Ne/χ for any composition of matter. The λ response vs. Ne/χ is depicted in FIGS. 1 a-1 d and illustrates maxima in λ at specific values of Ne/χ. By design or selection of compositions of matter which posses peak (near peak) λ values we are able to create novel compositions of matter that possess maximal values of T_(c) for their atomic properties as defined by Ne and χ of such a composition and by the consequence of a peak or near peak value of λ. Additionally we have developed a relationship by which we can estimate the value of the Debye temperature for any arbitrary composition of matter. This relationship is θ_(D) (Debye Temperature)=exp[10.0−0.64(ln at. wt.+ln at. vol)]. Additionally if the composition of matter is amorphous the θ_(D) as calculated above is modified to be equal to 0.70 θ_(D) (crystalline).

The values of Ne, χ (absolute electronegativity) and the (In at. wt.+ln at. vol) of selected elements as used in this invention are depicted in Table 1. Additionally, Table 2 illustrates the Ne/χ values at peak positions of λ and the peak value of λ and limits thereof.

TABLE I ln At. Metallic wt. + ln Absolute Atomic Valence At. Electronegativity no. Symbol Element Ne Vol. Electron Volts (χ) 1 H Hydrogen 1 2.67 7.18 2 He Helium 2 3 Li Lithium 1 4.5 3.00 4 Be Beryllium 2 4.25  4.6 ± 0.1 5 B Boron 3 4.5 4.29 6 C Carbon 4 4.34 6.26 7 N Nitrogen 5 5.49 7.3 8 O Oxygen 6 5.41 7.54 9 F Fluorine 7 5.79 10.41 10 Ne Neon 8 11 Na Sodium 1 6.30 2.84 12 Mg Magnesium 2 5.83 3.28 ± 0.5 13 Al Aluminum 3 5.60 3.21 14 Si Silicon 4 5.82 4.77 15 P Phosphorus 5 6.26 5.62 16 S Sulfur 6 6.26 6.22 17 Cl Chlorine 7 6.50 8.3 18 Ar Argon 8 19 K Potassium 1 7.48 2.42 20 Ca Calcium 2 6.94 3.07 21 Sc Scandium 3 6.49 3.37 22 Ti Titanium 4 6.23 3.46 23 V Vanadium 5 6.08 3.64 24 Cr Chromium 6 5.94 3.72 25 Mn Manganese 7 6.04 3.72 26 Fe Iron 8 5.98 4.02 27 Co Cobalt 9 5.87 4.27 28 Ni Nickel 10 5.96 4.39 29 Cu Copper 11 6.11 4.48 30 Zn Zinc 12 6.39 4.47 ± 0.1 31 Ga Gallium 3 6.70 3.21 32 Ge Germanium 4 6.89 4.56 33 As Arsenic 5 6.89 5.31 34 Se Selenium 6 7.17 5.89 35 Br Bromine 7 7.54 7.59 36 Kr Krypton 8 37 Rb Rubidium 1 8.47 2.33 38 Sr Strontium 2 8.01 2.87 39 Y Yttrium 3 7.27 3.26 40 Zn Zirconium 4 7.16 3.53 41 Nb Niobium 5 6.93 3.83 42 Mo Molybdenum 6 6.8 3.92 43 Tc Technetium 7 4.6 3.92 44 Ru Ruthenium 8 6.74 4.2 45 Rh Rhodium 9 6.74 4.3 46 Pd Palladium 10 6.84 4.45 47 Ag Silver 11 7.01 4.44 48 Cd Cadmium 12 7.28 4.43 ± 0.1 49 In Indium 3 7.50 3.1 50 Sn Tin 4 7.81 4.23 51 Sb Antimony 5 7.70 4.84 52 Te Tellurium 6 7.87 5.49 53 I Iodine 7 8.09 6.76 54 Xe Xenon 8 55 Cs Cesium 1 9.15 2.18 56 Ba Barium 2 8.59 2.67 57 La Lanthanum 3 8.05 3.02 58 Ce Cerium 4 7.95 3.25 59 Pr Praseodymium 3 8.03 3.21 60 Nd Neodymium 3 8.00 3.15 ± 0.1 61 Pr Promethium 3 8.09 3.21 ± 0.1 62 Sm Samarium 3 8.00 2.97 ± 0.1 63 Eu Europium 3 8.05 3.09 ± 0.1 64 Gd Gadolinium 3 8.05  3.1 ± 0.1 65 Tb Terbium 3 8.02 2.98 ± 0.1 66 Dy Dysprosium 3 8.03 3.02 ± 0.1 67 Ho Holmium 3 8.04 3.06 ± 0.1 68 Er Erbium 3 8.03 3.16 ± 0.1 69 Tm Thulium 3 8.03 3.61 70 Yb Ytterbium 3 8.36 3.63 71 Lu Lutetium 3 8.04 2.89 72 Hf Hafnium 4 7.79  3.7 ± 0.1 73 Ta Tantalum 5 7.59 4.11 74 W Tungsten 6 7.46 4.4 75 Re Rhenium 7 7.44 4.02 76 Os Osmium 8 6.10 4.89 77 Ir Iridium 9 7.41 5.33 78 Pt Platinum 10 7.48 5.56 79 Au Gold 11 7.60 5.77 80 Hg Mercury 12 7.99 5.12 81 Tl Thallium 3 8.17 3.24 82 Pb Lead 4 8.23 3.89 83 Bi Bismuth 5 8.41 4.12 84 Po Polonium 6 85 As Astatine 7 86 Rn Radon 8 87 Fr Francium 1 88 Ra Radium 2 89 Ac Actinium 3 90 Th Thorium 3, 4 8.47 3.55 ± 0.1 91 Pr Protactinium 3 92 U Uranium 3 8.01 3.15 ± 0.1 93 Np Neptunium 3 94 Pu Plutonium 3 28.2 3.25 ± 0.1

If no range is noted for the electronegativity the range is ±0.1 cv

TABLE II Ne/x values at peak (max λ) at indicated peak 0.465 ± .005  0.8 0.595 ± 0.004 1.0 0.655 + 0.001, −0.004 1.0  0.69 ± 0.003 0.80  0.74 ± 0.005 0.60 0.848 ± 0.001 0.55 0.875 ± 0.002 1.3  0.91 ± 0.002 1.2 0.971 ± 0.001 1.45 1.015 ± 0.002 2.85  1.07 ± 0.007 3.35 1.12 + 0.004, −0.01 2.6  1.17 ± 0.008 3.0 1.215 ± 0.002 2.45  1.28 ± 0.005 0.94 1.34 ± 0.01 0.95  1.36 ± 0.002 0.60 1.408 ± 0.003 0.90  1.45 ± 0.003 1.25 1.473 ± 0.002 0.75 1.508 ± 0.002 0.90 1.525 ± 0.002 0.55 1.578 ± 0.002 0.68 1.596 ± 0.002 0.55 1.642 + 0.005, −0.002 0.86 1.704 ± 0.005 0.68 1.80 + 0.00, −0.005 0.68 1.86 + 0.005 −0.01 0.74 1.97 ± 0.02 0.48 2.166 ± 0.01  0.65 2.16 ± 0.01 0.7 2.34 ± 0.01 0.90

All of the essential elements required to estimate the T_(c) of new and novel superconductors are now present and examples of their use for specific examples follows.

The actual novel compositions which are referred to later and in the claims are arrived at by tuning a particular composition of say, AB by selection of A′ or B′ or both from within the same class of elements constituting A or B such that A_(1-x)A′B or AB_(1-y)B′ or A_(1-x)A_(x)′B_(1-y)B_(y)′ such that the resultant composition is tuned to a single peak or near peak value of Ne/χ shown in Table 2 or FIG. 1 a-1 d, so as to maximize the electron phonon coupling constant. The natural result of such tuning exercise is to convert ternary to quaternary compositions or pentanary compositions and, to convert nominal ternary compositions to quaternary or pentanary compositions by the act of tuning to maximize the electron phonon coupling constant, and by the act of full or partial substitutions of A's and B's with elements of differing electronegativity such as to arrive a peak or near peak value of Ne/χ of such substituted composition of matter.

DETAILED DESCRIPTION OF THE INVENTION

The invention will be described in greater detail with reference to the drawing in which FIG. 1 a-1 d which is a plot of the electron phonon coupling constant λ against the values of Ne/χ which is dependent on the number of electron per atom in the composition and the absolute electronegativity.

By utilizing both the McMillan and the Allen-Dynes experimental results, and by limiting the values of λ derived from the McMillan equation to its range of validity, we arrive at a universal relationship between θ, T_(c), and λ. The plot of ln(θ_(D)/2 T_(c)) versus λ⁻¹ results in a (0,0) intercept, and in a universal equation for T_(c) which is

T _(c)=θ_(D)/2exp[−2/λ]

Similarly, using Allen-Dynes experimental results in amorphous superconductors and plotting ln(ωlog/2 T_(c)) vs. λ⁻¹, we arrive at

T _(c)=ωlog/2exp[−2/λ], wherein θ_(O), and ωlog are in units of ° K

The only difference in the two equations is the pre-exponential factor which represents the difference between crystalline superconductors in the McMillan case and amorphous superconductors in Allen-Dynes case. The dependence of T_(c) on λ remains in the same exponential form, that is, T_(c{EMBED Equation.3})exp[−2/λ].

With the above equation, we can calculate reliable values of λ for cuprate superconductors and a variety of other superconductors which heretofore has not been possible. For example, we calculate the λ values for several well-known superconductors, which are crystalline in nature, by both our universal equation and the McMillan equation, recalling that both equations are utilized at μ*=0.10. For La_(1.85)Sr_(0.15)CuO₄ whose T_(c)=38° K and whose θ_(D)=365° K, the McMillan equation results in λ=1.68 whereas for our universal equation λ=1.27. The McMillan result is ˜32% greater than that derived from the universal equation.

For YBa₂Cu₃O₇ whose T_(c)=92° K and whose θ_(D)=425 T_(c) the McMillan equation yields λ=24.1 whereas the universal equation yields a value if 2.39. The McMillan equation, which in this case is used well beyond its limits of validity, i.e. λ=0.90 differs from the universal equation value by an extremely high 1.008%.

For the highest T_(c) element Niobium, whose T_(c)=9.2° K and whose θ_(D)=277° K, the McMillan derived value of λ=0.745, whereas the value derived from the universal equation is λ=0.737 an insignificant difference of 1%.

In accordance with the present invention, we can calculate reliable values of λ. The λ values for various superconductors of arbitrary compositions can be connected to electronic properties of individual atoms which, in combination or individually, possess determinable atomic electronic properties. The two atomic properties we choose are Ne [the number of valence electrons/atoms] and χ the absolute electronegativity of individual atomic species

Where, χ[electronegativity]=I+A/2

Where I-ionization energy [ev]/atom and A is the electron affinity/atom in units of electron volts or [ev]/atom

From the preceding, we now note that an atomic property Ne/χ relevant to the electronic properties of atoms produce a reliable and reproducible response of λ vs. Ne/χ. The value λ can be shown to achieve peak values at particular values of Ne/χ, with either crystalline or amorphous superconductors as exemplified by the Allen-Dynes compounds or the elements of McMillan, and the cuprates as well. This accommodation of both amorphous and crystalline compounds illustrates the robustness of λ vs. Ne/χ. This robustness allows for the estimation of the λ value for any arbitrary compound by calculating the value of its Ne/χ value from its constituents and the use of the universal equation for T_(c) if θ_(D) is also known.

A reasonable estimate of θ_(D) can be made from the correlation of θ_(D) with the term [ln(atomic weight)+ln(atomic volume)]. Each element possesses unique values of the above terms. The value of ln(atomic weight)+ln(atomic volume) for any arbitrary compound is simply the geometric means of its constituents. The correlation equation is θ_(D)=e^(10−0.64 ln[(atomic weight)+ln(atomic volume)]). As an example, the θ_(D) for YBa₂Cu₃O₇ is equal to θχ^(10−0.64(6.11))=441° K and the experimental values is 447° K. For YBa₂Cu₃O₇ (ln atomic weight+n atomic volume)_(Y123)=7.27×(8.59)²×(6.111³×(541)⁷, the product thereof=[1.65×10¹⁰]^(1/13)=6.11 which is the geometric mean of the combined ln's of the atomic weight and atomic volume for the atomic constituents of YBa₂Cu₃O₇. A simpler example is that of Niobium whose (ln atomic weight+ln atomic volume)=6.93 Therefore,

θ_(D)(Nb)=e ^(10−0.64(6.93))=261° K,

whereas the literature value for Nb=277° K.

A more recent discovery relating to superconductor MgB₂ is found in an article by Akamitsu, Nature (London) 410, 63 (2001), which is incorporated herein by reference. The discovery of MgB₂ in 2001 by Akamitsu Lab was the result of a screening of compounds that had previously not been investigated for superconductivity. Commercially available samples of MgB₂ were available as early as the 1950's. There were succeeding attempts by the superconductor community to discover and produce other Magnesium Diborides. The compounds MgB₂ did not fit the Mathias rule, and there was no evidence of other similar compounds being superconductive. The discovery of MgB₂ was not based on scientific theory or available methodology to guide or to explore such a compound for superconductivity. As it turned out, MgB₂ which is superconductive at 40° K, has proven to be a useful discovery and maintains to this day the T_(c) record temperature for simple noncuprate superconductors. Directly after the discovery of MgB₂, there was a flurry of activity in the scientific community and two principle approaches were taken.

-   -   1. Doping of MgB₂ by substitution (either Mg substituted by Al         or Boron substituted by Carbon or Be) effects for both Mg and B,         while maintaining the MgB₂ structure. Examples were         Mg_(1-x)Al_(χ)B₂ and MgB_(2-χ) with χ being either Be or C.     -   2. The second approach was to screen or make isostructural         compounds which included the Borides of the elements (Li, Be,         Al) and the transition metal Borides Sc, Ti, Zr, Hf, V, Ta, Cr,         Mo and Nb. The report on TaB₂ by Rosner and Pickett in September         2001 with Ta borides. They produced two samples of Ta borides         namely, TaB_(1.26) and TaB_(2.03)

Both approaches provided no superconductivity.

For the above two specific samples, if we calculate the values of Ne/χ and θ_(D) from our graphical data, we can estimate the values of χ for these compositions and the values of θ_(D), and hence the expected superconducting critical temperature.

From the above values for these two compositions, we can calculate the estimated T_(c) in ° K.

For composition (1), graphically with the reference to FIGS. 1A-1D, λ is found to be 0.25 and θ_(D)=654° K and T_(c)=0.11° K by solving our universal equation. For composition (2), we find similarly that λ=0.25 and θ_(D)=718° K. Therefore, T_(c)=0.13° K. The referred paper by Rosner and Pickett provided measurements of these compounds to only 1.5° K. Thus superconductivity was not observed and according with our calculations, it should not have since, both estimated T_(c) values were less than 1.5° K.

A TaB₂ composition can be made to have a superconductor characteristic. For example, Ta_(1-χ)Ti_(χ)B₂ is found in the ternary composition range and also Ti_(0.65)Ta_(0.35)B₂ which has λ value graphically of ˜1.03 and an (Ne/χ) of about 0.847 and θ_(D)=829° K. Thus it can be computed that

T _(c)(Ti_(0.65)Ta_(0.35)B₂)≈88.9° K.

In accordance with this invention, we can establish accurate λ values if θ_(D) and T_(c) are known. The two equations that delineate the relationships are

T _(c)=θ_(D)/2exo[−2/λ] and

λ=[θ_(D)/2T _(c)/2]⁻¹

The following four examples satisfy these equations:

Composition Ne/χ θ_(D) Estimated λ T_(c) Nb_(1.95)Ti_(1.05)Sn 1.174 259° K 2.7  61° K Zr_(2.12)Nb_(0.88)Sn 1.122 210° K 2.5  41° K La_(1.20)Tm_(0.55)Sr_(0.15)CuO₄ 1.069 426° K 3.3 116° K Sc_(1.0)La_(0.85)Ca_(0.15)CuO₄ 1.071 486° K 3.3 132° K

Examples 1 and 2 are in the class of A-15 type compounds, i.e., AB₃ and should posses a high critical field ≧10 Telsa. The practical applications could be in the form of wires carrying large current densities at higher temperature than now realized. The advantage would be the relaxed refrigeration requirement; other refrigerants instead of Helium could be useful, liquid refrigerant instead of helium which could be useful in MRI type applications. The wires currently used are NbTi alloys having a T_(c) of ˜10-11° K and can operate only at liquid Helium temperatures.

Example 3 is a compound related to the original Bednorz-Mueller discovery of La_(1.85)Ba_(0.15)CuO₄ for which they won the Nobel Prize. The novel composition disclosed herein optimizes the Copper layer structure having nontoxic elements in its composition to achieve a T_(c)˜132° K which heretofore has only been obtained with compounds containing toxic elements, such as Mercury (Hg) and Thallium (Ti). Such compounds were more complex, containing three Copper layers per composition in contrast to the single Copper layer used in the novel composition disclosed herein. For example 3 and 4, the preparation process would preferably be conducted under high pressure to ensure the desired structure.

Another Example is the same class as preceding Examples 1 and 2.

EXAMPLE 4

Composition Ne/χ θ_(D) λ T_(c) V_(2.655)Nb_(0.345)Si 1.215 449° K ~2.45 99° K

This represents a composition in the A-15 class which has the potential to be refrigerated by liquid Nitrogen i.e. ˜77° K and would be expected to have a high critical field as well.

The following lists Examples of optimized Superconductive compositions:

Examples of Optimized Superconductive Compositions

Example 1: A-15 Type, V_(2.655)Nb_(0.345)Si_(0.885)Ge_(0.115)

-   -   Ne/χ=1.216; λ˜2.45; θ_(D)˜440° K; T_(c)˜97° K

Example 2: A-15 Type, Nb₃Ge_(0.245)Al_(0.755)

-   -   Ne/χ=1.216; λ˜2.45; θ_(D)307° K; T_(c)˜62° K

Example 3: MgB₂ Type, Mg_(0.8)Sc_(0.1)Na_(0.1)B₂

-   -   Ne/χ=0.656; λ˜1.0; θ_(D)˜940° K; T_(c)˜63° K

Example 3a: Cuprate, La_(1.33)Tm_(0.52)Sr_(0.15)CuO₄

-   -   Ne/χ=1.07; λ˜3.3; θ_(D)˜420° K; T_(c)˜109° K

Example 4: Cuprosulfide, Sc_(1.85)Sr_(0.15)CuS₄

-   -   Ne/χ=1.175; λ˜3; θ_(D)˜391° K; T_(c)˜100° K

Example 5: Cuproselenide, Sc_(1.85)Ba_(0.15)CuSe₄

-   -   Ne/χ=11.214; λ˜2.3; θ_(D)˜270° K; T_(c)˜56° K

Example 6: Intermetallic, Mg₂Ni_(0.53)Pt_(0.47)

-   -   Ne/χ=1.125; λ˜2.5; θ_(D)˜457° K; T_(c)˜101° K

Example 6a: Intermetallic, Mn_(0.90)Mo_(0.10) Al₁₂

-   -   Ne/χ=1.016; λ˜2.7; θ_(D)˜596° K; T_(c)˜142° K

Example 7: Cuprate, Mg_(0.765)Be_(0.135)CuO₂

-   -   Ne/χ=1.12; λ˜2.6; θ_(D)˜605° K; T_(c)˜140° K

Example 8: Bismuth Sulfide, Ba_(0.6)Na_(0.30)K_(0.10)BiS₃

-   -   Ne/χ=1.015; λ˜2.5; θ_(D)˜269° K; T_(c)˜60° K

Example 8a: Bismuth Selenide, Ba_(0.65)Rb_(0.35)BiSe₃

-   -   Ne/χ=1.063; λ˜3.0; θ_(D)˜63° K; T_(c)˜42° K

Example 9: Titanium Selenide, RbTi₂Se₄

-   -   Ne/χ=1.064; λ˜3.0; θ_(D)˜241° K; T_(c)˜61° K

Example 10: Cuprate, ScMg_(1.5)Ca_(0.5)Cu₃O₇

-   -   Ne/χ=1.124 λ˜2.5; θ_(D)˜557° K; T_(c)˜125° K

Example 11: Intermetallic, Mg₃Au_(0.81)Ag_(0.19)

-   -   Ne/χ=1.016; λ˜2.7; θ_(D)˜415° K; T_(c)˜99° K

Example 12: Cuprate, PdMgBe₂Cu₃O_(8.45)

-   -   NE/χ˜1.074; λ˜3.3; θ_(D)˜652° K; T_(c)˜177° K

Example 13: PdMg_(1.12)Be_(0.88)CuO_(4.15)

-   -   NE/χ˜1.069; λ˜3.3; θ_(D)˜626° K; T_(c)˜170° K

Example 14: Silicide, V_(0.59)Mo_(0.4)Si₂

-   -   NE/χ1.017; λ˜2.6; θ_(D)˜477° K; T_(c)˜1101K

Example 15: Intermetallic, Cr_(0.914)V_(0.086)Al₃

-   -   NE/χ˜1.12; λ˜2.50; θ_(D)˜578° K; T_(c)˜129° K

Example 16: Intermetallic Aluminum deficient, MoAl_(2.9)

-   -   NE/χ˜1.115; λ˜2.5; θ_(D)˜509° K; T_(c)˜114° K

Example 17: Cuprate (oxide) YMg₂Cu₃O₇

-   -   NE/χ˜1.117; λ˜2.5; θ_(D)˜552° K; T_(c)˜124° K

Example 18: CuproSulfide, YBe_(1.06)Mg_(0.94)Cu₃S₇

-   -   NE/χ˜1.215; λ˜2.45; θ_(D)˜476° K; T_(c)˜105° K

Example 19: Diboride, Sc_(0.6)La_(0.4)RuB₂

-   -   NE/χ˜1.069; λ˜3.3; θ_(D)˜621° K; T_(c)˜169° K

Example 20: Transition Metal MonoBoride, Ti_(0.98)V_(0.02)B

-   -   NE/χ˜0.91; λ˜1.2; θ_(D)˜744° K; T_(c)˜70° K

Example 21: Transition Metal Monoboride, V_(0.47)Cr_(0.53)B

-   -   NE/χ˜1.073; λ˜3.3; θ_(D)˜790° K; T_(c)˜215° K

Example 22: Transition Metal Pentaboride, Mo_(1.16)W_(0.84)B₅

-   -   NE/χ˜0.91; λ˜1.2; θ_(D)˜831° K; T_(c)˜78° K

Example 23: Transition Metal Pentaboride, Mo 78Ti_(0.22)B₅

-   -   NE/χ˜0.91; λ˜1.2; θ_(D)˜870° K; T_(c)˜82° K

Example 24: Transition Metal Tetraboride, Cr_(2.78)M_(0.22)B₄

-   -   NE/χ˜1.07; λ˜3.3; θ_(D)˜858° K; T_(c)˜234° K

Example 25: Boron Deficient Transition Metal Tetraboride, Cr₃B_(3.95)

-   -   NE/χ˜1.065; λ˜3.0; θ_(D)˜857° K; T_(c)˜220° K

Example 26: Intermetallic, Mg₂Si_(0.885)Sn_(0.115)

-   -   NE/χ˜0.652; λ˜1.0; θ_(D)˜510° K; T_(c)˜34° K

Example 27: Au_(0.95)Cu_(0.05)Be₃

-   -   NE/χ˜0.876; λ˜1.3; θ_(D)˜956° K; T_(c)˜102° K

Example 28: Intermetallic, Ti_(0.59)Nb_(0.25)V_(0.16)Al₃

-   -   NE/χ˜1.016; λ˜2.6; θ_(D)˜543° K; T_(c)˜126° K

Example 29: Cuprate, TmBe₂Cu₃O₇

-   -   NE/χ˜1.077; λ˜3.0; θ_(D)˜640° K; T_(c)˜161° K

Example 30: Boride, TiB_(0.98)

-   -   NE/χ˜0.91; λ˜1.2; θ_(D)˜907° K; T_(c)˜91° K

Example 31: Monoboride, Zr_(0.90)V_(0.10)B

-   -   NE/χ˜0.91; λ˜1.2; θ_(D)˜600° K; T_(c)˜56° K

Example 32: Monoboride, Cr_(0.60)Nb_(0.40)B

-   -   NE/χ˜1.07; λ˜3.3; θ_(D)˜725° K; T_(c)˜186° K

Example 33: Intermetallic, IrSn_(2.96-2.98)

-   -   NE/χ˜1.171; λ˜3.0; θ_(D)˜159° K; T_(c)˜41° K

Example 34: Intermetallic, Ir₃Sn_(6.9)

-   -   NE/χ˜1.215; λ˜2.6; θ_(D)˜161° K; T_(c)˜37° K

Example 35: A composition of matter specified by Re_(0.925)B₂,

-   -   NE/x=1.015, θ_(D) is 752° K, λ=2.8 and whose Tc=184° K.

Example 36: A composition of matter specified by Re_(0.55)B₂,

-   -   NE/x=0.913, θ_(D) is 893° K, λ=1.20 and whose Tc=84° K.

Example 37: A composition of matter whose composition is V_(0.82)B₂

-   -   NE/x=0.876, θ_(D) is 950° K, λ=1.3 and whose Tc=101° K.

Example 38: A composition of matter where composition is V_(0.655)B₂

-   -   NE/x=0.848, θ_(D) is 990° K, λ=1.3 and whose Tc=106° K.

Example 39: Alloys of Cu, Ni, Pt, Pd, Ir, Au, Ag C Ne/χ=2.34

Alloys Compound Ne/χ θ_(D) T_(c) Binary Ag_(.785)Au_(0.215) 2.34 233° K 12.7° K Pd_(0.55)Cu_(.45) 2.34 314° K 20.2° K Cu_(.81)Au_(.19) 2.34 374° K   20° K Ternary Cu_(.40)Pd_(.275)Ni_(0.325) 2.34 402° K   22° K Cu_(0.75)Pt_(0.1575)Ag_(0.925) 2.34 369° K   20° K Quaternary Cu₃Ag_(0.30)Au_(.385)Pt_(.315) 2.34 365° K 19.7° K Peranary Cu₃Ag_(0.225)Ir_(0.275)Au_(0.32)Pd_(0.18) 2.34 340° K 18.4° K Hexanary Cu₃Ag_(0.2625)Au_(0.3525)Pt_(0.1575)Ir_(0.1375)Pd_(0.09) 2.34 368° K 19.9° K

Example 40: A composition of matter where composition is Ta_(0.93)Zr_(0.07,)

-   -   NE/x=1.212, θ_(D)˜175° K, λ˜2.4 and whose T_(c)˜38° K.

Example 41: A composition of matter where composition is Ta_(0.93)Zr_(0.035)Ti_(0.035),

-   -   Ne/x=1.213, θ_(D)˜179° K, λ˜2.4 and whose T_(c)˜39° K. 

1. Superconductor compositions that are electrically conductive comprising a multiplicity of different species of atoms, characterized by having an Ne/χ value that is not a peak or near peak value of λ, where Ne is the average number of valence electrons in the composition, and χ is the absolute value of the electronegativity of the composition, and λ is the electron phonon coupling constant, wherein Ne/χ can be shifted to peak or near peak value by substitution or partial substitution of at least one of said species of atoms with an atomic species having and electronegativity different from at least one of said species of atoms which is being replaced by said substitution, said substitution resulting in a superconductive composition of matter. Ne/x values at peak or near peak values of one of the following Ne/x: 0.465±0.005, 0.595±0.004, 0.655+0.001, −0.004, 0.69±0.003, 0.74±0.005, 0.848±0.001, 0.875±0.002, 0.91±0.002, 0.971±0.001, 1.015±0.002, 1.07±0.007, 1.12±0.004, −0.01, 1.17±0.008, 1.215±0.002, 1.28±0.005, 1.34±0.01, 1.36±0.002, 1.408±0.003, 1.45±0.003, 1.473±0.002, 1.508±0.002, 1.525±0.002, 1.578±0.002, 1.596+0.002, 1.642+0.005, −0.009, 1.704±0.005, 1.80±0.00, −0.005, 1.86±0.005-0.01, 1.97±0.02, 2.166±0.01, 2.16±0.01, 2.34±0.01
 2. Superconductor compositions as in claim 1 represented by the A-15 or A₃B structure of inter metallic compounds wherein partial of multiple partial substitutions of the A and B components are affected to produce an Ne/χ value at a peak or near peak value of λ the electron phonon coupling constant. Such substitutions of either A or B components or both must result in one of the following values: Ne/χ=11.12±0.004, Ne/χ=1.17±0.008 or Ne/χ=1.215±0.002
 3. Superconductive compositions as in claim 1 relating to MgB₂ which are optimized to an Ne/χ value of 0.655+0.001, −0.004 and whose compositions are Mg_(0.80)Sc_(0.10)Na_(0.10)B₂ and Mg_(0.88)Sc_(0.06)Na_(0.06) and resulting in T_(c)'s of ˜64° K.
 4. Superconductor compositions as in claim 1 are superconductive compounds relating to the MnAl₁₂ structure in which MnAl₁₂ is nonstoichiometric by 1-2% in Mn or Al and wherein Mn or Al or both are partially substituted such that the resulting value of Ne/χ=1.015±0.002 and wherein the elements for partial substitution for Mn are Tungsten or Molybdenum or both.
 5. Superconductor compositions as in as claim 1 related to La_(1.85)Sr_(0.15)CuO₄ whose Ne/χ values are optimized to a peak value of Ne/χ represented by an Ne/χ value of 1.07_(—)0.008, −0.002, 1.17±0.008 or 1.215±0.002
 6. Superconductor compositions as in claim 1 consisting of intermetallic compositions of compounds A₃B where A is Mg and B is either Nickel or Palladium or both in any combination such that B is equal to unity and said A component (Mg) is necessarily slightly deficient such that it is equal to that A_(2.95±0.01) such that the Ne/χ value is at Ne/χ=1.015±0.002
 7. Superconductor compositions as in claim 1 represented by A₃B wherein A is equal to Aluminum and B is represented by an admixture of transition metal elements comprising Ti, Zr, Nb, V, Ta such that a peak or near peak value of λ represented by a specific value of Ne/χ is achieved so as to maximize the superconductivity critical temperature of the final composition and initially Al may be partially or fully substituted by Gallium. The resulting Ne/χ value that must be achieved is Ne/χ=1.015±0.002
 8. Superconductor compositions as in claim 1 wherein the protypical composition is A₂B wherein A is Magnesium and B is comprised of admixtures Si, Sn, Pb and Ge such that the resulting composition containing 2, 3 or 4 of such said components in the admixture result in an Ne/χ value of 0.655±0.001, −0.004 and have a peak λ value of ˜1.0.
 9. Superconductor compositions according to claim 1 where the protypical compound is Mo₂B₅ or W₂B₅ wherein an admixture of Mo and W resulting in Mo_(1.16)W_(0.84)B₅ is at a λ peak and at an Ne/χ value=0.91±0.002 and has a θ_(D)=830° K and a T_(c) of 78° K.
 10. Superconductor compositions as in claim 1 which are characterized by transition metal monodiborides wherein the transition metals consists of admixtures of greater than or equal to 2 atoms of the transition metal elements at individual concentrations such that the sum of all transition metal elements sum to unity transition metals represented by Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Re, Tc, Ru, Rh, Pt or Pd and that said combinations result in Ne/χ values corresponding to peak or near peak values of λ at one of the following designated Ne/χ values. Ne/χ=0.91±0.002, 1.015±0.002, 1.07±0.007 and 1.12+0.004, −0.01
 11. Superconductive compositions as in claim 1 comprising mixed Yttrium Scandium, La and rare earth, and Lutetium Diborides containing Ir or Ru in concentrations for each class of elements wherein the protypical compound ABC₂ where A=Y, La, Sc, rare earth elements and B=Ru or Ir and C=Boron said admixture of Y, La, Tm, Sc and other rate earth elements of two or more such elements in either Ir or Ru containing DiBorides are such that Ne/χ values representing a peak of in λ result. Said compositions result in peak or near peak λ values at Ne/χ represented by one of the following Ne/χ values; 1.12±0.009, −0.01, 1.07±0.007, −0.008 or 1.015±0.002
 12. Superconductor compositions as in claim 1 that are transition metal Trialuminides i.e. (TM=Transitional Metal) Al₃ wherein the transition metal component is a mixture of two or three transition metals whose sum is unity and whose combination for is set by the necessity to achieve a peak or near peak value of λ at one of the following values of Ne/χ 1.015±0.002, 1.07±0.007 or −0.008, 1.12±0.009 or −0.01, 1.17±0.008, 1.215±0.003 or 1.28±0.005
 13. Superconductor composition according to claim 1 that Mo, V, Cr or Ta and Silicon as mixed transition metal disilicides consists of compounds achieving peak or near peak λ values at specific values of Ne/χ are V_(0.59)Mo_(0.41)Si₂ and Ta_(0.45)Cr_(0.53)Si₂ both at Ne/χ=1.015±0.002.
 14. Superconductor compositions are in claim 1 having the structure A₂B where A is Mg and B is Ni, Pd or Pt wherein for Ni and Pt B=0.99 and B may be multiply substituted such that the resulting composition is formed Mg 2 Pt 0.54 Ni 0.46 wherein one of the following Ne/χ must be achieved Ne/χ=1.07, 0.0007, 0.008, 1.12+0.009, −0.01 or 1.17±0.008.
 15. Superconductor compositions as in claim 1 wherein Sulfides and Selenides are substituted into Ba₆K₄BiO₃ and wherein either Sulfur or Selenium replace the Oxygen of said Ba_(0.6)K_(0.4)BiO₃ and wherein Ne/χ values at peak or near peak values are achieved. Alkaline earth elements Ba, Sr, Ca, Mg balanced against alkaline elements Li, Na, K and Rb and said combinations are combined with S or Se replacing O so as to achieve one of the following peak or near peak values of Ne/χ. Ne/χ1.07±0.008 or 1.015±0.002
 16. A superconductor composition that is electrically conducting comprising: A multiplicity of different species of atoms characterized by having a Ne/χ value that is at a peak or near peak value of Ne/χ where Ne is the number of valance electrons and χ is the absolute electronegativity of the composition and λ is the electron phonon coupling constant. Such composition is a superconductor by virtue of its Ne/χ value and which is at a peak or near peak value of Ne/χ. Such composition can be shifted to a peak or near peak value of Ne/χ adjacent to its present peak by substitution or partial substitution of at least one of its atomic constituents by atomic species of ln valence or differing electronegativity or both such that the Ne/χ value of said substituted composition is at an adjacent Ne/χ value represented by one of the following values of Ne/χ. Wherein such said composition is characterized by one of the following values of Ne/χ: 0.465±0.005, 0.595±0.004, 0.655±0.001, 0.69±0.003-0.004, 0.74±0.005, 0.848±0.001, 0.875±0.002, 0.91±0.002, 0.971±0.001, 1.015±0.002, 1.07±0.007, 1.12±0.004, −0.01, 1.17±0.008, 1.215±0.002, 1.28±0.005, 1.34±0.01, 1.36±0.002, 1.408±0.003, 1.45±0.003, 1.473±0.002, 1.508±0.002, 1.525±0.002, 1.578±0.002, 1.596±0.002, 1.642+0.005, −0.002, 1.704±0.005, 1.80±0.00, −0.005, 1.86+0.005−0.01, 1.97±0.02, 2.166±0.01, 2.16±0.01, 2.34±0.01.
 17. Superconductor composition based upon LiTi2O4 according to claim 16 wherein Oxygen is replaced by Sulfur or Selenium or a combination thereof and the Li is replaced by appropriate levels of the following alkaline earth elements Na, K, or Rb such that the final composition of said Sulfide, Selenide, or mixed Sulfoselenide results in Ne/χ value of 1.015±0.002 or 1.07±0.008.
 18. Superconductor compositions according to claim 16 that are analogs of the cuprate family specified by AB₂C_(n-1)Cu_(n)O_(2n+2+8) wherein A is the element Palladiuim and δ≈0.1-0.15n wherein for n=1 B=Sr, n=2 B=2Sr and C=Sr for n=3 both B=25 and C=2Sr, for n=4 B=4Sr and C=1Ca for n=5 B=4Sr and C=2Ca for n=6 B=4Sr and C=3Ca and for n=7 B=4Sr and C=4Ca this series of Pd cuprates have Ne/χ values ranging from 1.169 to 1.177 i.e. essentially constant Ne/χ value of the maximal Ne/χ value of 1.17±0.008.
 19. Superconductor composition based upon claim 16 wherein said superconductor composition is based upon YBa₂Cu₃O₇ wherein the Oxygen atoms are substituted by Sulfur and the Y can be any rare earth element or La and Ba is replaced by a combination of Ca, Mg, or Be such that the resulting composition is at a peak or near peak value of Ne/χ represented by: Ne/χ=1.215±0.002 or 1.17±0.008
 20. Superconductor composition related to YBa₂Cu₃O₇ as in claim 16 wherein Y is substituted with the trivalent rare earth or admixtures thereof in combination with appropriate levels either solely, or as admixtures such that the combination of rare earth component and the alkaline earth component results in an Ne/χ peak or near peak value. The said alkaline earths are represented by Be, Mg, Ca, Sr or Ba at concentrations such that the following peak or near peak values of Ne/χ are achieved. Such peak or near peak values of said compositions at different peak or near peak values of Ne/χ then the parent YBa₂Cu₃O₇. The Ne/χ values that must be achieved are 1.12+0.009, −0.01 and 1.215±0.002
 21. Superconductor compositions as in claim 16 comprising A₃B compounds wherein A is Magnesium and B is Cu, Ag or Au and wherein the A component is at 2.9±0.02 for B equal to Au, and 2.97±0.01 for B=Cu and for B equal to Silver A is in the range of 2.98-3.05, said concentrations of A with corresponding B's are set to equal peak or near peak values of Ne/χ. Similarly the A component can be held to exactly 3.0 with admixtures of Cu, Ag, and Au so as to produce peak or near peak values of Ne/χ which are 1.07±0.008 and 1.015±0.002
 22. Superconductor compositions as in claim 16 wherein the parent compound YBa₂Cu₃O₇ is modified with combinations of rare earth elements such as Sc, Y and La either alone and/or in combination. They are combined with substitution of Ba by Be, Ca, Mg and Sr alone or in combination with before said substitutions of Yttrium such that the resulting overall substituted compositions achieves in different peak or near peak value than the protypical YBa₂Cu₃O₇ wherein said final overall combinations result in peak or near peak values of λ represented by Ne/χ value of affording said peak values of λ these Ne/χ values are one of which must be achieved are 1.12±0.008 and 1.07±0.008.
 23. Superconductor compositions as in claim 16 wherein these compositions are related to YBa₂Cu₃O₇ but are substituted in the Y and Ba components such that the resulting peak or near peak values of λ represented by different Ne/χ values than the protypical YBa₂Cu₃O₇ wherein Sc or B substitute for Y and Be, Mg, Ca, substitute in appropriate amounts for Ba such that peak or near peak values of λ are combined at different Ne/χ values than YBa₂Cu₃O₇ these Ne/χ values are 1.07±0.008.
 24. Superconductor compositions as in claim 16 wherein the peak value of AuBe₃ is shifted from Ne/χ of 0.873 to 0.875 or 0.91 wherein the Gold is substituted partially by either Copper, Silver or both such that peak λ at Ne/χ=0.875±0.001 or 0.91±0.002 are achieved.
 25. Superconductor composition as in claim 16 consisting the transition metal tetraborides Cr₃B₄ and Mn₃B₄ and therein the combined (CrMn)₃ wherein the Mn/Cr ratio can be adjusted as to yield two or more completely different compositions with different peak or near peak values of λ and two different values of Ne/χ which are respectively. Ne/χ=1.12+0.004, −0.001 and Ne/χ=1.015±0.002.
 26. Superconductor compositions as in claim 16 wherein the protypical and stoichiometric compound Mn₃B₄ and Cr₃B₄ are optimized by rendering their Ne/χ value to values at the peak or near peak of λ by formulating slight non stoichiometery in the Boron component of the compounds such that the following formations apply M₃B_(3.96-3.98) Ne/χ˜1.17± and Cr₃B_(2.93-2.97) such that Ne/χ=1.17± and whose Ne/χ value at peak λ at ÷1.17±0.008.
 27. Superconductor compositions as in claim 16 that are related to MoAl₃ and CrAl₃ and require nonstoichiometric adjustments or composition to affect Ne/χ values that are at a peak value of λ. These compositions are as follows: Cr_(0.96)Al₃ and MoAl_(2.90) such that Ne/χ value of 1.12±0.009, −0.01 is achieved.
 28. Superconductor compositions according to claim 16 which is nonstoichiometric said superconductor composition is Zr₅Si_(2.9) whose Ne/χ value=1.015±0.002.
 29. Superconductor compositions as in claim 16 containing Ir₃Sn_(7-x) where x is between 0.002 and 0.005 said compositions having a value of Ne/χ=1.213 and where λ value is ˜2.6 and where θ_(D) is 161° and where T_(c)˜34° K.
 30. Superconductor compositions as in claim 16 comprising of IrM₃ where M is a combination of Silicon and Tin such that the total number of Si and Sn atoms sum to 2.95 to 3.0 and wherein such a compositions has an Ne/χ value equal to 1.12, a θ_(D)˜265° and a T_(c) value of 59° K.
 31. Superconductor compositions as in claim 16 comprising IrM_(3-x) wherein said M₃ is comprised of Germanium and Tin such that said elements Ge and Sn sum to a total of 2.9 to 3.0 atoms in said IrM_(3-x) wherein χ=0 to 0.005 where Ne/χ value=1.113 and where λ˜2.50 and where θ_(D)=237° and T_(c)=58°
 32. Superconductor compositions that is binary and electrically conductive containing one of the following transition metals, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, T_(c), and also Re, and wherein the additional element is either Carbon, Nitrogen or Boron and wherein the resulting transition metal monocarbides and transition metal monoborides and mononitrides and transition metal diborides are deficient in the transition metal component such that said transition metal deficiency results in an Ne/χ value within its associated limits such that a maximum value of λ within it's limits results in a maximum or near maximum value of Tc. Said values of the transition metal must fall between 0.99 and 0.5 and be adjusted to a concentration within this range so as to achieve one of the following values of Ne/χ within its associated limits. Said, values of Ne/χ are; 0.848±0.001, 0.875±0.002, 0.91±0.002, 1.015±0.005, and 1.07±0.008.
 33. Superconductor compositions as in claim 32 whose composition is Ti_(0.915)C, whose Ne/x=0.848, θ_(D) is 811° K and whose λ=1.3 and whose Tc=87°.
 34. Superconductor compositions as in claim 32 which is Mg_(1-x)Zn_(x)B₂ is made with x=0.01Zn that is Mg_(0.99)Zn_(0.01)B₂ whose Ne/x=0.655, λ˜1.0, θ_(D)˜953° K and Tc=64° K.
 35. Superconductor compositions as in claim 32 whose composition is V_(0.84)C and whose Ne/x=0.912, θ_(D) is 862° K and whose λ=1.2 and whose Tc=81° K.
 36. Superconductor compositions as in claim 32 whose composition is Ta_(0.745)N, and whose Ne/x=0.875, θ_(D) is 389° K, λ=1.3 and whose Tc=41° K.
 37. Superconductor compositions as in claim 32 whose composition is Re_(0.912)C Ne/x=1.072, θ_(D) is 606° K, λ=3.0 and whose Tc=155° K.
 38. A composition of matter according to claim 32 whose composition is Re 0.733 C whose Ne/x=1.015, θ_(D) is 673° K, λ=2.8 and whose Tc˜˜164° K.
 39. Superconductive compositions that are electrically conductive and amorphous, wherein the amorphicity is induced by at least one of the following atomic species, Be, B, Si, Ge, or P and the metallicity is provided by a combination of at least one of the following elements: Y, Sc, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, T_(c), Mn, R^(e), W, Fe, Ru, Os, Co, Rh, Ir, Ni. Pd, Pt, Cu, Ag, Au, Zn, Cd, or Hg, wherein said compositions contain at least 10 total atomic percent of the said amorphicity inducing element, the remaining percentage of said composition consisting of one or more of said metallicity inducing elements, wherein said final composition must achieve one of the following Ne/χ values: 0.655+0.001, −0.004, 0.69±0.003, 0.875±0.002, 0.91±0.002, 0.971±0.001, 1.015±0.002, 1.07±0.007, 1.12+0.004, −0.0 1, 1.17±0.008, 1.215±0.002, 1.642+0.005, −0.002 or 2.34±0.01
 40. An amorphous composition of matter as in claim 39 whose composition is Ti_(0.51)Nb_(0.15)V_(0.20)Si_(0.084)B_(0.05), Ne/χ=1.168, λ=3.0, θ_(D)˜300° K, Tc˜77° K.
 41. Superconductor compositions as in claim 39 defined by Be_(0.40)Mo_(0.05)Re_(0.55), Ne/χ=1.168, λ=3.0, θ_(D)˜348° K, Tc˜89° K.
 42. An amorphous composition of matter as in claim 39 defined by Be_(0.39)W_(0.015)Ti_(0.055)Cr_(0.50)Mo_(0.04), Ne/χ=1.073 λ=3.0, θ_(D)˜527° K, Tc˜135° K.
 43. An amorphous composition of matter as in claim 39 defined by Ti_(0.44)V_(0.15)Si_(0.21)B_(0.020), Ne/χ=1.014, λ=2.8, θ_(D)˜392° K, Tc˜95° K.
 44. An amorphous composition of matter as in claim 39, defined by Ti_(0.50)V_(0.15)Nb_(0.15)B_(0.10)Si_(0.11), Ne/χ=1.124, λ=2.6, θ_(D)˜310° K, Tc˜71° K
 45. A superconductive composition containing at least two elements wherein the major element is not at a peak value of Ne/χ and wherein partial substitution of the major element by one or more elements of differing valence and or electronegativity result in a composition whose Ne/χ value at one of the following Ne/χ values; Ne/χ values, 0.465±0.005, 0.595±0.004, 0.655±0.001-0.004, 0.848±0.001, 0.875±0.002, 0.91±0.002, 1.015±0.002, 1.07±0.007, 1.12+0.004−0.01, 1.172±0.008, 1.215+0.002-0.004, 1.28±0.005, 1.34±0.01, 1.408±0.003, 1.45±0.003, 1.508±0.002, 2.34±0.01
 46. A superconductive composition as in claim 45 containing Tantalum at 0.88 to 0.95 atomic fraction with the balance being 0.05 to 0.12 atomic percent of Titanium or Zirconium or any mixture thereof said Titanium or Zirconium.
 47. A superconductive composition as in claim 45 whose composition is Zr₃Hf and whose Ne/χ=1.12, λ˜2.5; θ_(D)˜229° K; T_(c)˜51° K.
 48. A superconductive composition as in claim 45 whose composition is LuLa and whose Ne/χ=1.0115; λ˜2.6; θ_(D)˜128° K; T_(c)˜29° K. 